Bipolarons and superconductivity

2014 The problem of deformation induced attraction leading to localized pairs of electrons, the so-called bipolarons, is studied in detail. The analogy between bipolarons and itinerant Cooper pairs in a superconductor is explored. It is shown that the two types of pairing result from the microscopic nature of the electron-phonon Hamiltonian and that following the coupling constant the ground-state becomes a bipolaronic insulator beyond a critical coupling strength. A phase diagramme between a metal, superconductor and bipolaronic insulator is proposed. J. Physique 42 (1981) 1351-1356 SEPTEMBRE 1981, Classification Physics Abstracts 71. 38 74.20 Introduction. In a series of recent papers [1], we have pointed out the fundamental interest of the bipolaronic ground-state defined as a localized pair of electrons coupled through lattice deformation. The experimentally observed bipolarons, the charge localization, their insulator-metal transition and other physical properties have been dealt with at length [2]. We have also recently [3] suggested that there is a fundamental symmetry between this bipolaronic ground-state and a superconducting ground-state because these bipolarons can be considered as localized Cooper pairs in the limit of large electron-phonon coupling constant. A phase diagramme between metal-superconductor and bipolaronic insulator has been proposed that reflects the increasing instability of the metallic electrons at the Fermi level to attractive pairing interaction due to strain-induced coupling. In part 1 of this paper, we shall briefly recall the essential results of electron pairing due to static strain while in part 2 we shall describe in some detail the dynamic Hamiltonian and will show that the electron-phonon Hamiltonian contains within its very structure two complementary parts one of which gives rise to bipolaron formation while the other part leads to superconductivity. Part 3 will be a succinct discussion of some of the points still obscure. 1. Pairing due to static strain. It is easy to see why strain is essential if one is to form a pair of localized electrons in a singlet ground-state out of two itinerant electrons in an empty band. In figure la, a one-dimensional chain of identically spaced atoms are indicated, with near-neighbour transfer integral t. The total energy for two electrons in an otherwise empty band is then where eo is the single-site energy of an electron. Were we to localize these two electrons in a pair of undeformed neighbouring atoms (Fig. lb) into the singlet state, the ground-state energy will be where v is the near-neighbour Coulomb repulsion between the two electrons and J is the exchange integral between two sites. We note that v > J, E2 is larger than E 1 (DE = E2 E i is positive) and hence E2 can never be a ground-state for the two electrons. On the other hand, if we relax